The rules you mentioned are correct,
turnover applies both to own and to enemy pieces.
But the illegal move Ke8xd8 doesn't look like a
turnover (in this case, that would be a combinination
King + Queen to a completely new piece),
but looks like a castling King - Queen.
Moreover, the King has already all 3 rings, so all
ring-combinations including that of the Queen are
already integrated in him. So he can
be separated into two different pieces, but there
is no piece to combine with him for a turnover -
such a turnover would result in a piece not
existing in chess
The rules you mentioned are correct, turnover applies both to own and to enemy pieces.
But the illegal move Ke8xd8 doesn't look like a turnover (in this case, that would be a combinination King + Queen to a completely new piece), but looks like a castling King - Queen.
Moreover, the King has already all 3 rings, so all ring-combinations including that of the Queen are already integrated in him. So he can be separated into two different pieces, but there is no piece to combine with him for a turnover - such a turnover would result in a piece not existing in chess